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Wavelet-based procedures are key in many areas of statistics,
applied mathematics, engineering, and science. This book presents
wavelets in functional data analysis, offering a glimpse of
problems in which they can be applied, including tumor analysis,
functional magnetic resonance and meteorological data. Starting
with the Haar wavelet, the authors explore myriad families of
wavelets and how they can be used. High-dimensional data
visualization (using Andrews' plots), wavelet shrinkage (a simple,
yet powerful, procedure for nonparametric models) and a selection
of estimation and testing techniques (including a discussion on
Stein's Paradox) make this a highly valuable resource for graduate
students and experienced researchers alike.
Through its scope and depth of coverage, this book addresses the
needs of the vibrant and rapidly growing engineering fields,
bioengineering and biomedical engineering, while implementing
software that engineers are familiar with. The author integrates
introductory statistics for engineers and introductory
biostatistics as a single textbook heavily oriented to computation
and hands on approaches. For example, topics ranging from the
aspects of disease and device testing, Sensitivity, Specificity and
ROC curves, Epidemiological Risk Theory, Survival Analysis, or
Logistic and Poisson Regressions are covered. In addition to the
synergy of engineering and biostatistical approaches, the novelty
of this book is in the substantial coverage of Bayesian approaches
to statistical inference. Many examples in this text are solved
using both the traditional and Bayesian methods, and the results
are compared and commented.
This volume provides a thorough introduction and reference for any researcher who is interested in Bayesian inference for wavelet-based models, but is not necessarily an expert in either. To achieve this goal the book starts with an extensive introductory chapter providing a self-contained introduction to the use of wavelet decompositions and the relation to Bayesian inference. The remaining papers in this volume are divided into six parts: independent prior modeling; decision theoretic aspects; dependent prior modeling; spatial models using bivariate wavelet bases; empirical Bayes approaches; and case studies. Chapters are written by experts who published the original research papers establishing the use of wavelet-based models in Bayesian inference. Peter Müller is Associate Professor and Brani Vidakovic is Assistant Professor of Statistics at Duke University.
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